Propagation of near-limit gaseous detonations in small diameter tubes

In this study, detonation limits in very small diameter tubes are investigated to further the understanding of the near-limit detonation phenomenon. Three small diameter circular tubes of 1.8, 6.3, and 9.5 mm inner diameters, of 3 m length, were used to permit the near-limit detonations to be observed over long distances of 300 to 1500 tube diameters. Mixtures with high argon dilution (stable) and without dilution (unstable) are used for the experiments. For stable mixtures highly diluted with argon for which instabilities are not important and where failure is due to losses only, the limit obtained experimentally appears well to be in good agreement in comparison to that computed by the quasi-steady ZND theory with flow divergence or curvature term modeling the boundary layer effects. For unstable detonations it is suggested that suppression of the instabilities of the cellular detonation due to boundary conditions is responsible for the failure of the detonation wave. Different near-limit propagation regimes are also observed, including the spinning and galloping mode. Based on the present experimental results, an attempt is made to study an operational criterion for the propagation limits of stable and unstable detonations.     

高浓度氩气稀释气体爆轰波临界管径和临界间距关系

建立圆管及环形管道系统研究临近极限下爆轰波在管道内传播失效机理。选用C₂H₂+2.5O₂+70%Ar气体,采用光纤探针测量爆轰波在管道内传播速度,用烟迹法记录管道内爆轰波胞格结构。结果表明:初始压力远大于爆轰极限压力时,爆轰波在管道内以稳定速度传播;随着初始压力的减小,爆轰波速度逐渐降低;当初始压力一定时,爆轰波速度随着管道尺寸的减小而逐渐减小;当初始压力达到临界压力时,爆轰波在进入到管道内后其速度会逐渐衰减直至爆轰波完全失效。对于不同几何尺寸的圆管与环管,通过引入无量纲参数d/λ及w /λ(d为圆管管径,w为环管间距,λ为爆轰胞格尺寸)得出,爆轰波在管道内传播的临界圆管直径为环形间距的2倍,与理论模型结果相吻合,验证了稳态气体基于爆轰波波面曲率的失效机理。     

Detonation diffraction from an annular channel

In this study, gaseous detonation diffraction from an annular channel was investigated with a streak camera and the critical pressure for transmission of the detonation wave was obtained. The annular channel was used to approximate an infinite slot resulting in cylindrically expanding detonation waves. Two mixtures, stoichiometric acetylene–oxygen and stoichiometric acetylene–oxygen with 70% Ar dilution, were tested in a 4.3 and 14.3 mm channel width (W). The undiluted and diluted mixtures were found to have values of the critical channel width over the cell size around 3 and 12 respectively. Comparing these results to values of the critical diameter (d _c ), in which a spherical detonation occurs, a value of critical d _c /W _c near 2 is observed for the highly diluted mixture. This value corresponds to the geometrical factor of the curvature term between a spherical and cylindrical diverging wave. Hence, the result is in support of Lee’s proposed mechanism [Lee in Dynamics of Exothermicity, pp. 321, Gordon and Breach, Amsterdam, 1996] for failure due to diffraction based on curvature in stable mixtures such as those highly argon diluted with very regular detonation cellular patterns.     

Investigation of the detonation regimes in gaseous mixtures with suspended starch particles

The existence of a secondary discontinuity at the rear of a detonation front shown in experiments by Peraldi and Veyssiere (1986) in stoichiometric hydrogen-oxygen mixtures with suspended 20-m starch particles has not been explained satisfactorily. Recently Veyssiere et al. (1997) analyzed these results using a one-dimensional (1-D) numerical model, and concluded that the heat release rate provided by the burning of starch particles in gaseous detonation products is too weak to support a double-front detonation (DFD), in contrast to the case of hybrid mixtures of hydrogen-air with suspended aluminium particles in which a double-front detonation structure was observed by Veyssiere (1986). A two-dimensional (2-D) numerical model was used in the present work to investigate abovementioned experimental results for hybrid mixtures with starch particles. The formation and propagation of the detonation has been examined in the geometry similar to the experimental tube of Peraldi and Veyssiere (1986), which has an area change after 2 m of propagation from the ignition point from a 69 mm dia. section to a 53 mm 53 mm square cross section corresponding to a 33% area contraction. It is shown that the detonation propagation regime in these experiments has a different nature from the double-front detonation observed in hybrid mixtures with aluminium particles. The detonation propagates as a pseudo-gas detonation (PGD) because starch particles release their heat downstream of the CJ plane giving rise to a non-stationary compression wave. The discontinuity wave at the rear of the detonation front is due to the interaction of the leading detonation front with the tube contraction, and is detected at the farthest pressure gauge location because the tube length is insufficient for the perturbation generated by the tube contraction to decay. Thus, numerical simulations explain experimental observations made by Peraldi and Veyssiere (1986). Received 5 July 1997 / Accepted 13 July 1998     

Detonation Initiation by Shock Reflection from an Orifice Plate

Results from an experimental investigation of the interaction of a “non-ideal” shock wave and a single obstacle are reported. The shock wave is produced ahead of an accelerated flame in a 14 cm inner-diameter tube partially filled with orifice plates. The shock wave interacts with a single larger blockage orifice plate placed 15–45 cm after the last orifice plate in the flame acceleration section of the tube. Experiments were performed with stoichiometric ethylene–oxygen mixtures with varying amounts of nitrogen dilution at atmospheric pressure and temperature. The critical nitrogen dilution was found for detonation initiation. It is shown that detonation initiation occurs if the chemical induction time based on the reflected shock state is shorter than the time required for an acoustic wave to traverse the orifice plate upstream surface, from the inner to the outer diameter. The similarity between the present results and those obtained from previous investigators looking at detonation initiation by ideal shock reflection produced in a shock tube indicates that the phenomenon is not sensitive to the detailed structure of the shock front but only on the average shock strength.This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

孔板扰动对爆轰波胞格结构特性影响的实验研究

实验采用稳定预混气2H₂+O₂+3Ar及不稳定预混气C₂H₂+5N₂O和CH₄+2O₂,在圆形爆轰管内通过烟膜手段记录了爆轰波的胞格结构,得到了胞格尺寸与初始压力之间的关系式;研究了胞格结构在扰动上下游的变化过程,分析了胞格不稳定性对胞格结构特征的影响,获得了爆轰波经过扰动后重新恢复至平衡状态的特征尺度。结果表明:爆轰波经过扰动后,对于稳定预混气,在扰动下游主胞格结构变得不规则,没有出现次生胞格;对于不稳定预混气,扰动下游伊始爆轰波的次生模态被抑制,由于爆轰波自身的不稳定性,随后出现了局部爆炸点及精细胞格结构;爆轰波在扰动下游传播了一段距离后恢复至平衡状态,该长度在8～15倍之间的胞格尺寸范围内变化,并且随初始压力的变化趋势并不明显。研究结果反映出爆轰波经过孔板扰动后恢复至平衡态所需的长度与爆轰波流体动力学厚度相当。     

On the propagation mechanism of a detonation wave in a round tube with orifice plates

This study deals with the investigation of the detonation propagation mechanism in a circular tube with orifice plates. Experiments were performed with hydrogen air in a 10-cm-inner-diameter tube with the second half of the tube filled with equally spaced orifice plates. A self-sustained Chapman–Jouguet (CJ) detonation wave was initiated in the smooth first half of the tube and transmitted into the orifice-plate-laden second half of the tube. The details of the propagation were obtained using the soot-foil technique. Two types of foils were used between obstacles, a wall-foil placed on the tube wall, and a flat-foil (sooted on both sides) placed horizontally across the diameter of the tube. When placed after the first orifice plate, the flat foil shows symmetric detonation wave diffraction and failure, while the wall foil shows re-initiation via multiple local hot spots created when the decoupled shock wave interacts with the tube wall. At the end of the tube, where the detonation propagated at an average velocity much lower than the theoretical CJ value, the detonation propagation is much more asymmetric with only a few hot spots on the tube wall leading to local detonation initiation. Consecutive foils also show that the detonation structure changes after each obstacle interaction. For a mixture near the detonation propagation limit, detonation re-initiation occurs at a single wall hot spot producing a patch of small detonation cells. The local overdriven detonation wave is short lived, but is sufficient to keep the global explosion front propagating. Results associated with the effect of orifice plate blockage and spacing on the detonation propagation mechanism are also presented.     

Dynamics study of detonation-wave cellular structure 1. Statistical properties of detonation wave front

We have investigated the evolution of cellular detonation-wave structure as a gaseous detonation travels along a round tube and measured cell lengths as a function of the initial pressure of the gas. We have tested acetylene-containing combustible gas mixtures with different degrees of regularity. Along with the smoked-foil technique, an emission method has been used to the measure current and average values of the detonation cell length. The method is based on the detection of an emission spectrum behind the detonation front in the spectral range corresponding to local gas temperatures that are much higher than those for the Chapman-Jouguet equilibrium condition. This technique provides quasi-continuous cell-length measurements along the normal to the detonation front over the length of several factors of ten times the tube. Our study has experimentally identified the steady states of detonation structure in round tubes, referred to here as the single detonation modes. When the state of a single mode is fully established, then both the flow structure and the energy release at detonation front develop strictly periodically along the tube at a constant frequency inversely proportional to the cell length of the mixture. The mixture regularity has had no influence on the occurrence of the detonation mode, which is defined by the value of initial pressure or the total energy release of the mixture. Outside of the pressure range where a detonation mode was most likely to occur, the detonation front is unstable and may exhibit an irregular cellular pattern. Monitoring the evolution of cells over a long distance revealed that the local gas emissivity, which is time dependent and corresponds to axial pulsations of the detonation structure, has the appearance of a superposition of separate harmonics describing the states of emissivity oscillations and cell structure of single detonation modes. Received 18 October 1999 / Accepted 10 June 2001     

Experimental investigation into the detonation characteristics of hybrid RDX–ethylene–air mixtures

An experimental study is conducted to determine the detonation characteristics of 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) particles dispersed in a gaseous fuel air mixture in a vertical detonation tube with an inner diameter of 200 mm and a height of 5400 mm. Experiments are performed in both ethylene–air mixtures and RDX–ethylene–air hybrid mixtures. The detonation front pressure and velocity are measured with six pressure transducers along the detonation tube. The results show that the addition of RDX assists 4.0 vol.% ethylene–air mixtures in achieving detonation. The detonation front pressure increases noticeably with dust concentration up to \(474\hbox { g/m}^{3}\) in the RDX–ethylene–air hybrid mixtures, but the velocity only increases slightly. The cellular structures of RDX–ethylene–air hybrid mixtures and ethylene–air mixtures were obtained with the use of smoked foils and exhibit irregular structures. It is found that the measured cell size has a U-shaped curve with respect to RDX concentration.     

Mach reflection in detonations propagating through a gas with a concentration gradient

In accident scenarios where detonations can occur a concentration gradient constitutes a more realistic initial condition than a perfectly homogeneous mixture. In this paper, the influence of a concentration gradient on detonation front shape, detonation instabilities and pressure distribution is studied. First, a simple method to determine the front shape from a given fuel distribution is presented. It is based on Huygens’ principle and includes a correction to satisfy the boundary conditions on the enclosing walls. Next, the presented highly resolved Euler computations demonstrate the influence of a concentration gradient on detonation instabilities. In configurations with a strong concentration gradient, Mach reflection occurs and leads to an asymmetric pressure load on the enclosing geometry. In this case, the impulse on the wall is higher than in configurations with homogeneous fuel distribution, although the fuel content is much lower.     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Effect of initial disturbance on the detonation front structure of a narrow duct

The effect of an initial disturbance on the detonation front structure in a narrow duct is studied by three-dimensional numerical simulation. The numerical method used includes a high-resolution fifth-order weighted essentially non-oscillatory scheme for spatial discretization, coupled with a third-order total variation diminishing Runge-Kutta time-stepping method. Two types of disturbances are used for the initial perturbation. One is a random disturbance which is imposed on the whole area of the detonation front, and the other is a symmetrical disturbance imposed within a band along the diagonal direction on the front. The results show that the two types of disturbances lead to different processes. For the random disturbance, the detonation front evolves into a stable spinning detonation. For the symmetrical diagonal disturbance, the detonation front displays a diagonal pattern at an early stage, but this pattern is unstable. It breaks down after a short while and it finally evolves into a spinning detonation. The spinning detonation structure ultimately formed due to the two types of disturbances is the same. This means that spinning detonation is the most stable mode for the simulated narrow duct. Therefore, in a narrow duct, triggering a spinning detonation can be an effective way to produce a stable detonation as well as to speed up the deflagration to detonation transition process.     

In-plane perturbation of the tunnel-crack under shear loading I: bifurcation and stability of the straight configuration of the front

One considers a planar tunnel-crack embedded in an infinite isotropic brittle solid and loaded in mode 2+3 through some uniform shear remote loading. The crack front is slightly perturbed within the crack plane, from its rectilinear configuration. Part I of this work investigates the two following questions: Is there a wavy “bifurcated” configuration of the front for which the energy release rate is uniform along it? Will any given perturbation decay or grow during propagation? To address these problems, the distribution of the stress intensity factors (SIF) and the energy release rate along the perturbed front is derived using Bueckner–Rice's weight function theory. A “critical” sinusoidal bifurcated configuration of the front is found; both its wavelength and the “phase difference” between the fore and rear parts of the front depend upon the ratio of the initial (prior to perturbation of the front) mode 2 and 3 SIF. Also, it is shown that the straight configuration of the front is stable versus perturbations with wavelength smaller than the critical one but unstable versus perturbations with wavelength larger than it. This conclusion is similar to those derived by Gao and Rice and the authors for analogous problems.     

Comparison of critical conditions for DDT in regular and irregular cellular detonation systems

Abstract. The results of an experimental study of DDT in mixtures with regular and irregular detonation cellular structures are presented. Experiments were carried out in a tube 174 mm i. d. with obstacles (blockage ratios were 0.1, 0.3, and 0.6). Mixtures used were hydrogen–air and stoichiometric hydrogen–oxygen diluted with , Ar, and He. The critical conditions for DDT are shown to depend on the regularity of the cellular structure of test mixtures. The critical values of the cell sizes in Ar- and He-diluted mixtures are shown to be significantly smaller than those in -diluted mixtures. This means that systems with a highly regular detonation cellular structure have far less capacity for undergoing DDT compared to irregular ones with the same values of detonation cell sizes. Received 18 November 1999 / Accepted 15 May 2000     

Numerical study of three-dimensional detonation structure transformations in a narrow square tube: from rectangular and diagonal modes into spinning modes

Three-dimensional (3-D) detonation structure transformations from rectangular and diagonal modes into spinning modes in a narrow square tube are investigated by high-resolution simulation. Numerical simulations are performed with a Riemann solver of the HLLC-type, new cell-based structured adaptive mesh refinement data structure, high-order, parallel adaptive mesh refinement reactive flow code. A simplified one-step kinetic reaction model is used to reveal the 3-D detonation structure. The four different types of initial disturbances applied in the ZND profiles lead to the structures of rectangular in phase, rectangular out of phase, rectangular partial out of phase and diagonal, respectively, during the initial stages of detonation propagation. Eventually, all these detonation structures evolve into the self-sustained spinning detonations. The asymmetric disturbance leads to a stable spinning detonation much faster than the rest. The important features in the formation of spinning detonation are revealed using a 3-D visualization, and a remarkable qualitative agreement with experimental and numerical results is obtained with respect to the transverse wave dynamics and detonation front structures. The transverse wave collisions produce the unburnt gas pockets and the energy to sustain the detonation front propagation and distortion. The periodic pressure oscillation of front plays a complex role as it shifts the reaction zone structure with an accompanying change in the driving energy of transition and the detonation parameters which result in the more distorted front and the unstable detonation. Eventually, the unstable distorted detonation evolves into a spinning detonation.     

Cellular detonations in bidispersed gas-particle mixtures

Formation of cellular detonation in bi-fractional stoichiometric mixtures of aluminum particles and oxygen is investigated numerically. The detonation cell size depends on the particle diameters and relative concentration of the fractions. Certain degeneration of cellular detonation is obtained when compared to the monodisperse mixtures. It is characterized by maximal pressure decrease, transverse wave relaxation and detonation front rectification. Complete degeneration of cellular detonations and stable propagation of a plane detonation front is found in some bi-fractional mixtures. The numerical results are confirmed by acoustic analysis of the detonation structures. This paper is based on work that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

弯管内爆轰波传播的流场显示和数值模拟

采用激光纹影系统拍摄了爆轰波在不同位置的流场照片. 用二阶附加半隐的龙格- 库塔法和五阶WENO格式 分别离散欧拉方程时间和空间导数项,用基元反应来描述爆轰化学反应过程,获得了压力、 温度、典型组元质量分数分布及数值胞格结构和爆轰波平均速度. 结果表明：受壁面稀疏波 和压缩波影响,爆轰波阵面发生畸变. 但由于弯管曲率半径较大,未出现爆轰波熄灭. 靠近 凹壁面的激波强度大于凸壁面侧,且凹壁面侧的反应区宽度较凸壁面侧要窄. 弯管出口处的 三波点数目较入口处减少,爆轰波衰减. 在出口直段,受扰动的爆轰波可恢复为自持爆轰波. 爆轰波流场、胞格结构、平均爆轰波速度的计算和实验结果定性一致.     

氢气/丙烷/空气预混气体爆轰性能的实验研究

通过采用压力传感器和烟灰板两种测试设备,开展了常温常压下氢气/丙烷和空气混合气体爆轰性能的实验研究。实验过程中观察到自持爆轰波,爆轰速度比值在0.99~1之间,爆轰压力比值在0.8~1.2之间。爆轰胞格尺寸在10~50 mm范围内,建立了爆轰胞格尺寸和化学诱导长度的关系式。随着丙烷不断添加,爆轰速度减小,而爆轰压力和胞格尺寸增加。这种变化趋势起初较快,而后变缓。因为起初氢气摩尔分数较大,混合气体趋向于氢气/空气的爆轰性能;而后因丙烷摩尔质量较大,丙烷逐渐起主要作用,混合气体表现出丙烷/空气的爆轰性能。     

直管内胞格爆轰的基元反应数值研究

基于基元反应和二维欧拉方程，对直管内胞格爆轰进行了数值模拟。采用5阶WENO(weighted essentially nonoscillatory scheme)求解对流项，采用2阶附加半隐的龙格-库塔法处理化学反应源相引起的刚性。获得了密度、压力、温度和典型组元质量分数流场及数值胞格结构等。结果表明:网格精度的差异明显影响胞格的规则性和爆轰的平衡模数，随着网格尺度的减小，胞格由不规则变为规则。预混气组成、初压、初温及管道宽度给定，三波点数收敛为确定值。足够强度的初始扰动可再现胞格爆轰，最终形成的自持胞格爆轰模数与初始扰动的形状、大小、位置均无关。沿胞格中心线，爆轰波速度变化范围为0.88DCJ~1.5DCJ，爆轰波平均速度与CJ爆轰速度仅偏差0.88％。峰值压力与初压之比为14~50。计算爆轰波平均速度、胞格宽长比与实验值基本一致，但计算胞格宽度比实验值略小。数值模拟加深了对横波的产生和发展、未反应气囊、爆轰胞格的二次起爆等胞格爆轰特性的认识。     

爆轰波在阻尼管道中声吸收的实验研究

实验旨在研究气相爆轰波在阻尼管道 (管壁上衬有吸收材料 )中传播时的衰减现象。先是在光滑管壁的管道中产生稳定的具有胞格结构的爆轰波 ,然后使其通过专门设计的管壁上衬有吸收材料 (金属丝网或不锈钢纤维 )的阻尼段。利用高速摄影、压力传感器和烟迹技术等手段 ,记录和测试了阻尼段对几种混合气体爆轰波的传播速度、爆压及胞格结构产生的影响。实验分别在方管和圆管中进行。发现在某些条件下爆轰波可以被衰减成强爆燃。